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38
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
 COMPUTERAIDED GEOMETRIC DESIGN
, 2005
"... In this paper, we propose a new quadrilateral remeshing method for manifolds of arbitrary genus that is at once general, flexible, and efficient. Our technique is based on the use of smooth harmonic scalar fields defined over the mesh. Given such a field, we compute its gradient field and a second v ..."
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Cited by 73 (2 self)
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In this paper, we propose a new quadrilateral remeshing method for manifolds of arbitrary genus that is at once general, flexible, and efficient. Our technique is based on the use of smooth harmonic scalar fields defined over the mesh. Given such a field, we compute its gradient field and a second
QUADRILATERAL REMESHING AND EFFICIENT SURFACE PARAMETERIZATION
, 2007
"... Surface remeshing is a fundamental problem in computer graphics, and can be found in most digital geometry processing systems. The majority of work in this area has focused on remeshing with triangle elements, yet quadrilateral meshes are best suited for many occasions, such as physical simulation a ..."
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and defining CatmullClark subdivision surfaces. In the first part of this work, we propose a quaddominant remeshing method based on the use of a smooth harmonic scalar function defined over the surface. Given such a field, we compute its gradient field and a second vector field that is everywhere orthogonal
Harmonic homogeneous manifolds of nonpositive curvature
, 2004
"... A Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point of the manifold is radial. Flat and rankone symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for manifolds of nonnegative scalar curvature an ..."
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A Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point of the manifold is radial. Flat and rankone symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for manifolds of nonnegative scalar curvature
A class of nonsymmetric harmonic Riemannian spaces
 Bull. Amer. Math. Soc
, 1992
"... Abstract. Certain solvable extensions of Htype groups provide noncompact counterexamples to a conjecture of Lichnerowicz, which asserted that “harmonic ” Riemannian spaces must be rank 1 symmetric spaces. A Riemannian space M with LaplaceBeltrami operator ∆ is called harmonic if, given any functio ..."
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Cited by 49 (0 self)
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function f(x) on M depending only on the distance d(x, x0) from a given point x0, then also ∆f(x) depends only on d(x, x0). Equivalently, M is harmonic if for every p ∈ M the density function ωx0(x) expressed in terms of the normal coordinates around the point x0 is a function of d(x, x0) (see [1, 11
Multilinear Evolution Equations for TimeHarmonic Flows in Conformally Flat Manifolds
, 1996
"... Abstract It is shown that timeharmonic hypersurface motions in various, conformally flat, Ndimensional manifolds admit a multilinear description, L ˙ = {L, M1, · · ·, MN−2}, automatically generating infinitely many conserved quantities, as well as leading to new (integrable) matrix equations. I ..."
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(t, ϕ 1, · · ·, ϕ M) the (closed) hypersurface Σt (in a parametric description), ϕ 1, · · ·, ϕ M being local coordinates on a (compact) M = N − 1 dimensional Riemannian manifold Σ (on which the x i are timedependent functions), √ g the volume density (on Σt) induced by the embedding Riemannian
Multilinear Evolution Equations for TimeHarmonic Flows in Conformally Flat Manifolds
, 1996
"... Abstract It is shown that timeharmonic hypersurface motions in various, conformally flat, Ndimensional manifolds admit a multilinear description, L ˙ = {L, M1, · · ·, MN−2}, automatically generating infinitely many conserved quantities, as well as leading to new (integrable) matrix equations. I ..."
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(t, ϕ 1, · · ·, ϕ M) the (closed) hypersurface Σt (in a parametric description), ϕ 1, · · ·, ϕ M being local coordinates on a (compact) M = N − 1 dimensional Riemannian manifold Σ (on which the x i are timedependent functions), √ g the volume density (on Σt) induced by the embedding Riemannian
LTH 832 Instantons, black holes, and harmonic functions
, 906
"... We find a class of fivedimensional EinsteinMaxwell type Lagrangians which contains the bosonic Lagrangians of vector multiplets as a subclass, and preserves some features of supersymmetry, namely the existence of multicentered black hole solutions and of attractor equations. Solutions can be expr ..."
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of harmonic functions if an integrability condition is met. This condition can either be solved by imposing that the solution depends on a single coordinate, or by imposing that the target space is a paraKähler manifold which can
Instantons, black holes and harmonic functions,” arXiv:0906.3451 [hepth
"... Abstract: We find a class of fivedimensional EinsteinMaxwell type Lagrangians which contains the bosonic Lagrangians of vector multiplets as a subclass, and preserves some features of supersymmetry, namely the existence of multicentered black hole solutions and of attractor equations. Solutions c ..."
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Cited by 12 (3 self)
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in terms of harmonic functions if an integrability condition is met. This condition can either be solved by imposing that the solution depends on a single coordinate, or by imposing that the target space is a paraKähler manifold which can be obtained from a real Hessian manifold by a generalized r
Regularity of generalized sphere valued pharmonic
, 2003
"... Abstract. We prove (see Theorem 1.3 below) that a generalized harmonic map into a round sphere, i.e. a map u ∈ W 1,1loc (, Sn−1) which solves the system div (ui∇uj − uj∇ui) = 0, i, j = 1,..., n, is smooth as soon as ∇u  ∈ Lq for any q> 1, and the norm of u in BMO is sufficiently small. Here, ..."
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Abstract. We prove (see Theorem 1.3 below) that a generalized harmonic map into a round sphere, i.e. a map u ∈ W 1,1loc (, Sn−1) which solves the system div (ui∇uj − uj∇ui) = 0, i, j = 1,..., n, is smooth as soon as ∇u  ∈ Lq for any q> 1, and the norm of u in BMO is sufficiently small. Here
Hyperspherical Harmonics for Polyatomic Systems: Basis Set for Kinematic Rotations
, 2001
"... ABSTRACT: In a symmetrical hyperspherical framework, the internal coordinates for the treatment of Nbody systems are conveniently broken up into kinematic invariants and kinematic rotations. Kinematic rotations describe motions that leave unaltered the moments of the inertia of the Nbody system an ..."
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and perform the permutation of particles. This article considers the corresponding expansions of the wave function in terms of hyperspherical harmonics giving explicit examples for the fourbody case, for which the space of kinematic rotations (the “kinetic cube”) is the space SO(3)/V4 and then the related
Results 1  10
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38